Scaling law for natural convection heat transfer in supercritical fluids considering the vapor-like-layer effect

Available experiments on supercritical fluids have shown a vapor-like-layer effect during natural convection heat transfer (NCHT); however, a quantitative description of this effect remains challenging. Here, numerical simulations of NCHT were performed using a horizontal platinum wire heater with a 70-μm diameter and 22.0-mm length, immersed in a large supercritical carbon dioxide (sCO 2 ) pressure vessel. The results were in good agreement with the experimentally measured values. A physical model consisting of a vapor-like-layer region and a bulk fluid region was proposed to locate the interface between the two regions at the pseudo-critical temperature T pc . Unlike in previous studies, supercritical NCHT was treated via natural convection mechanism in the bulk fluid region, represented by a modified Rayleigh number Ra m , and with a heat transfer deterioration number De to reflect the vapor-like-layer effect. Our simulations, with pressures, heat fluxes, and wall temperatures in the ranges of 8–16 MPa, 112–917 kW/m 2 , and 334–672 K, yielded a correlation for Nusselt number Nu of the form N u = 1.92 ⋅ R a m 0.22 D e , thus providing a scaling law of Nu ∼ De , and a self-similarity characteristic of non-dimensional vapor-like-layer size R S * . These scaling laws are applicable to sCO 2 heat transfer with other parameter ranges and even for supercritical water. The correlation-predicted Nu was in good agreement with the experimental data, even though these data were not involved in the development of the correlation. Thus, our work presents new scaling laws to effectively understand the underlying mechanism and increases the prediction accuracy of supercritical NCHT.